Supporting Information

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Supporting Materials and Methods
Supporting Table 1
Supporting Table 2
Supporting Figure 5
Supporting Figure 6
Supporting Figure 7
Supporting Figure 8
Supporting Figure 9
Supporting Figure 10
Supporting Figure 11
Supporting Figure 12
Supporting Figure 13
Supporting Figure 14
Supporting Figure 15
Supporting Figure 16
Supporting Scheme 2

Fig. 5. UV/Vis absorption data for 1:1 ratios of [CBPQTÌS3]•4PF₆ (green trace), [CBPQTÌS4]•4PF₆ (yellow trace), and a mixture of S5 and CBPQ•4PF₆ (blue trace). All solutions were 2.5 mM in Me₂CO. Inset is a picture of the three solutions and shows the dramatic difference in the ability of the CBPQT⁴⁺ ring to form [2]pseudorotaxanes with S3 (green cap), S4 (yellow cap), and S5 (blue cap).

Fig. 6. ¹H NMR spectra of [CBPQTÌS3]•4PF₆ (2:1 CD₃CN/CD₂Cl₂, 238 K) (A) and [CBPQTÌS4]•4PF₆ (3:1 CD₃CN/CD₃COCD₃, 275 K) (B). The CBPQT•4PF₆ protons are highlighted in blue, and the S3 and S4 protons are highlighted in red. Signals arising from complexed and uncomplexed species are given the designation C and UC, respectively.

Fig. 7. ¹H NMR spectra of a mixture of S5 and CBPQT•4PF₆ (CD₃COCD₃, 298 K) (A) and the [2]rotaxane S6•4PF₆ (CD₃COCD₃, 298 K) (B). The CBPQT•4PF₆ protons are highlighted in blue, and the S5 protons are highlighted in red. The symmetry imposed heterotopicity of the CBPQT⁴⁺ protons and the change in chemical shift for signals associated with the dumbbell can clearly be seen in B.

Fig. 8. Schematic diagram illustrating the setup used for modeling the ground-state energy profile for deslipping of the CBPQT⁴⁺ ring over the end groups of single-station threads with 2,6-dimethyl- (S3), 2,6-diethyl- (S4), and 2,6-diisopropylphenyl ether (S5) end groups.

Fig. 9. Energy profiles plotted as relative energy (kcal•mol^–1) vs. distance (Å) as generated from molecular simulations of the deslipping of the CBPQT⁴⁺ ring off S3 (A), S4 (B), and S5 (C).

Fig. 10. Schematic diagram illustrating the setup used for the molecular force-field simulations.

Fig. 11. Crystal structures of [CBPQT][PF₆]₄ (A), TTF (B), [TTF•][ClO₄]₂ (C), and the [CBPQTÌTTF][PF₆]₄ complex (D) used for quantum mechanical calculations. PF₆^– and ClO₄^– counterions have been replaced with Cl^– atoms (green) to decrease computational cost. Hydrogen atoms have been omitted for clarity.

Fig. 12. Front (A) and profile (B) views of the calculated electrostatic potential surface for the hexacationic [CBPQTÌTTF] complex used to determine relative placement of additional counterions (red, greater electron density; blue, less electron density).

Fig. 13. Front (A) and profile (B) views of one of the five model systems used to determine the electrostatic repulsion between CBPQT⁴⁺ and TTF²⁺. Model systems were created by adding two additional Cl^– counterions (green) to the crystal structure of [CBPQTÌTTF][4PF₆], with Cl^– counterions in place of PF₆^–.

Fig. 14. Representative force trace of an Au-coated AFM tip bound to surface immobilized rotaxane R⁴⁺ in the presence of oxidant. (A and B) Force vs. Z piezo position (A) with zoom of rupture (B). (C and D) Force vs. tip/surface separation distance (C) with zoom of rupture (D). Force at rupture is 140 pN at a tip separation distance from the surface of 5.5 nm.

Fig. 15. Geometries and relative energies (in parenthesis with units of kcal•mol^–1) obtained from UB3LYP/6-31G* optimization of TTF (A), homolysis product 1 (B), homolysis product 2 (C), TTF²⁺ (D), TTF²⁺ homolysis product 1 (E), TTF²⁺ homolysis product 2 (F), and product obtained from rupture of the central C–C bond of TTF²⁺ (G). Energies of B and C are relative to TTF, and energies of E–G are relative to TTF²⁺. Two relevant geometrical parameters, the central C–C bond distance (in red with units of Å) and the 1-2-3-4 torsion angle (in blue with units of degrees), are highlighted for structures A–F.

Fig. 16. Histogram of compiled AFM force spectroscopy data of [2]rotaxane R⁴⁺ obtained in a solution of 10^–6 M Fe(ClO₄)₃ in EtOH (loading rate of 6 pN/s).

Scheme 2. Reaction schemes illustrating the synthesis of 2,6-diethylphenol (S1) (A), the dumbbell-shaped compounds S3–S5 (B), and the [2]rotaxane S6•4PF₆ (C).

Supporting Materials and Methods

Semiquantitative analysis of the slipping/deslipping processes of the CBPQT⁴⁺ ring onto/off S3 and S4 was accomplished using dynamic ¹H NMR spectroscopy. Spin saturation transfer (SST) (6) was used to determine the rate of slipping/deslipping for [CBPQTÌS3]•4PF₆ in the slow-exchange regime. Well resolved signals, corresponding to both complexed as well as uncomplexed DNP protons, can be observed within the temperature range, 260–323 K. Measuring the rate of exchange between complexed and uncomplexed DNP signals with SST gave the following energy barriers (Table 1) for slipping/deslipping: 15.4 kcal•mol^–1 (269 K), 16.5 kcal•mol^–1 (281 K), 17.8 kcal•mol^–1(304 K).

Exchange of complexed and uncomplexed DNP signals of [CBPQTÌS4]•4PF₆ could not be observed by SST, indicating that the slow-exchange regime for slipping/deslipping is not within the temperature range for which well resolved signals could be observed. Therefore, the bimolecular reaction kinetics associated with [2]pseudorotaxane formation were measured directly by ¹H NMR spectroscopy. Solutions of S5 and CBPQT•4PF₆ (2.5 mM in CD₃COCD₃) were mixed and the formation of [CBPQTÌS4]•4PF₆ was monitored over time, at both 273 and 296 K. In both cases, the probe temperature was calibrated with MeOH as well as tuned and locked using a solution of neat CD₃COCD₃. Solutions of the separate ring and dumbbell components were kept at 273 K and 296 K before mixing. Equal amounts of the ring and dumbbell solutions were mixed in an NMR tube and ¹H NMR spectra were recorded over a period of 240 min in one case (273 K) and 160 min in the other (296 K). The decrease in intensity of signals for the uncomplexed dumbbell and the appearance of signals for complexed dumbbell allowed determination of the bimolecular reaction kinetics. Plotting the inverse of uncomplexed dumbbell concentration (mM) vs. time (s) gave a straight line where the slope was equal to the rate of slipping. Using this method, rates of 0.027 s^–1 and 0.036 s^–1 were obtained at 273 and 296 K, respectively. They correspond (Table 1) to slipping barriers of 17.9 kcal•mol^–1 (273 K) and 19.3 kcal•mol^–1 (296 K), respectively.

The same combination of molecular dynamics and mechanics used to generate the ground-state energy profile (Fig. 4) of R⁴⁺ was used to model the deslipping of the CBPQT⁴⁺ ring off S3–S5. In all cases, a "dummy" atom was placed at a fixed distance from the model systems and constraints were used to "pull" the CBPQT⁴⁺ ring along the dumbbells (Fig. 8), which were constrained to be linear, in specified increments. A 50-ps molecular dynamics simulation (1.5-fs time step) at a simulation temperature of 500 K, followed by energy minimization of 200 randomly selected co-conformations, was used for co-conformational searching at each fixed distance along the dumbbell reaction coordinate. The output of each step was then used as the input for the next. Energies were normalized relative to the lowest energy co-conformationer of S3–S5, corresponding to the CBPQT⁴⁺ ring encircling the DNP unit in each case. The process was repeated in reverse to correct for any hysteresis. Computational results were compiled to generate ground-state energy profiles for deslipping (Fig. 9). Computations predicted energy barriers (Table 1) for deslipping over the 2,6-dimethylphenyl ether, 2,6-diethylphenyl ether, and 2,6-diisopropylphenyl ether end groups to be 17.5, 21.0, and 43.5 kcal•mol^–1 at 298 K, respectively. The theoretically calculated deslipping barriers are in good agreement with the experimentally measured ones for the [2]pseudorotaxanes [CBPQTÌS3]•4PF₆ and [CBPQTÌS4]•4PF₆. These results lend support to the conclusion that the theoretically predicted barrier of 43.5 kcal•mol^–1 for deslipping over the 2,6-diisopropylphenyl ether stopper should be a very good guide to the experimental value to which we cannot gain access in solution.

Theoretical modeling provides an important link between thermally activated deslipping of the CBPQT⁴⁺ ring over the 2,6-diisopropylphenyl ether stopper in solution, which cannot be obtained, and mechanically activated deslipping under the load of an AFM tip, which has been measured (Fig. 3a). All attempts to measure this barrier in solution have demonstrated that the barrier is too high to be measured experimentally, indicating that the mechanical bond is quite strong. Single-molecule force spectroscopy, however, has shown that rupture of R⁴⁺ occurs at a force (74 pN) that is an order of magnitude less than that required to rupture covalent bonds or the Au–S bond. Although the work done by an AFM tip distorts the system’s energy landscape, preventing a direct corollary between force and energy through distance, the barrier of 43.5 kcal•mol^–1 (or 46.0 kcal•mol^–1 when the CBPQT⁴⁺ ring originates from TTF) predicted by theoretical modeling sheds much-needed light on the R⁴⁺ system. A barrier on the order of 40 kcal•mol^–1 is, indeed, too high to be accessed thermally but sufficiently low to be measured mechanically under the load of an AFM tip, before the rupture of any covalent or Au–S bonds. The general agreement between theory and experiment, which has been established through slipping/deslipping studies of model compounds, adds greater support to the conclusion that the barrier to deslipping over the 2,6-diisopropylphenyl ether stopper is being modeled well and that single-molecule force measurements in the absence of a chemical oxidant are measuring deslipping of the CBPQT⁴⁺ ring over the 2,6-diisopropylphenyl ether stopper.

A combination of molecular dynamics and molecular mechanics was used to model the ground-state energy profile for R⁴⁺ as a function of position of the CBPQT⁴⁺ ring along the linear dumbbell as described in Materials and Methods in the main text.

Quantum mechanical single point calculations were used to predict the electrostatic repulsion between CBPQT⁴⁺ and TTF²⁺ based upon available x-ray crystal data for the free and complexed species (Fig. 11) as well as for five model systems for the hexacationic complex (Figs. 12 and 13). The computational procedure is described in the Materials and Methods in the main text. The five model systems, which differ in the placement of the two additional Cl^– counterions in the hexacationic complex, produced the following range of values for the repulsive electrostatic interaction between CBPQT⁴⁺ and TTF²⁺: 70.56, 72.65, 75.40, 75.90, and 76.7 kcal•mol–1.

AFM experimental analysis is critically contingent on the ability to specifically bind the gold-coated AFM tip to the CBPQT⁴⁺ ring’s disulfide-ended tether through the formation of thiol bonds. Although molecular extension analysis would be appropriate to verify this condition, we were only able to use this as a qualitative check for specific binding. Because the uncertainty of the molecular binding location on a typical AFM tip is unknown, no quantitative analysis is possible, especially given that the maximum length of the fully stretched [2]rotaxane R⁴⁺ is only »8 nm. Instead, various experimental conditions that were found to be critical to the experiment strongly indicate that we are specifically binding to rotaxanes on the surface. It was found that specific bonds, as seen in ruptures that were measured when the tip was no longer in contact with the substrate (Fig. 14), were only found after the gold-coated AFM tip was cleaned in a Harrick plasma cleaner using air for »90 s, indicating that clean and exposed gold was required for bonds to form. Moreover, specific bonds required the experiment to be conducted in a nonaqueous solution. Again, this supported the assertion that thiol bonds were being formed since in an aqueous environment [2]rotaxane R⁴⁺ would fold because of its hydrophobic end groups (7), precluding the disulfide tether from being available to the tip for bond formation. Further evidence supporting specific thiol bond formation lies in the fact that probing regions saw decreases in their yield after prolonged probing, due to the destruction of available rotaxanes for binding and probing. As would be expected, a change in probing region renews the previous yield levels. Lastly, it was observed that yields dropped after significant probing regardless of probing region indicating that the tip had become saturated with ruptured molecules. All of these indicators supplement the use of nearly 1,000 data points, which alone should minimize the contribution of nonspecific binding to the tip.

Force spectroscopy of relevant covalent bonds at loading rates of the same order of magnitude (»10 nN•s^–1) as our experiments (6 nN•s^–1) have shown covalent bond rupture forces to exceed our measured values by at least an order of magnitude, as seen in Table 2, which is a compilation of covalent bond rupture energies (8), distances [covalent bond rupture is expected to occur at around twice the equilibrium bond distance; therefore, rupture distances are reported as the equilibrium distance from Smith and March (8)], and forces (9–12) for all covalent single bonds present in the experiment as well as for the Au–Au bond. The effect of oxidation of TTF on covalent bond strength also was investigated.

Bond rupture energies and rupture distances for C–S bonds in TTF and oxidized TTF as well as the rupture energy and rupture distance of the central C–C bond in oxidized TTF were calculated using the program GAUSSIAN 03 (13) by employing the UB3LYP method and 6-31G* basis set. Computations were done in the gas phase, and frequency calculations were used to correct for zero-point and thermal energies. Bond energies were calculated as the difference in energy between optimized TTF (Fig. 15) and homolysis products (HP-1 and HP-1 in Fig. 15) corresponding to the rupture of the two different C–S bonds in TTF. Likewise, the bond energies of the two different C–S bonds and the central C–C bond of TTF²⁺ were calculated. Results of these calculations revealed bond energies of 55.3, 55.5, 54.7, 55.1, and 54.6 kcal•mol^–1 for the two C–S bonds in TTF, two C–S bonds of TTF²⁺, and central C–C bond of TTF²⁺, respectively. The small energetic difference (0.9 kcal•mol^–1) between bond energies reveal that the bond strengths are essentially equivalent and that oxidation of TTF does not significantly change the bond energies of C–S bonds, and only affects the strength of the central C–C bond of [2]rotaxane R⁴⁺. These theoretical values, along with the energetic barrier to deslipping as calculated from molecular force field simulations, are also given in Table 2. Although the work done by an AFM’s tip distorts the system’s energy landscape and, as a result, a direct corollary between force and energy through distance cannot be established (see reference 28 of the manuscript), the large disparity between the rupture energies and rupture distances of covalent bonds and those associated with deslipping (i.e., rupture of the mechanical bond) allow for general conclusions to be drawn between the two. As can be seen in Table 2, the rupture of covalent bonds is energetically costly and occurs over short distances. Deslipping of the CBPQT⁴⁺ ring over the bulky stopper, however, is a relatively low energy process that occurs over a distance that is at least 3.5 times greater than that required to rupture covalent bonds or the gold–sulfur bond, indicating rupture should occur at a lower force (9). Therefore, it is believed that the 74-pN rupture is due to deslipping of the CBPQT⁴⁺ ring over the bulky stopper resulting in rupture of the mechanical bond of R⁴⁺ as shown in Fig. 2a.

In addition to the performing AFM force spectroscopy probing experiments in an EtOH solution of 10^–4 M Fe(ClO₄)₃, preliminary probing experiments were conducted at a concentration of 10^–6 Fe(ClO₄)₃. The histogram of compiled AFM force spectroscopy data of [2]rotaxane R⁴⁺ obtained in a solution of 10^-6 M Fe(ClO₄)₃ in EtOH (loading rate of 6 pN/s) is shown in Fig. 16. The black curve is obtained from commercial peak-finding and curve-fitting algorithms and indicates a singular peak rupture force of 104 pN. Although this indicates a slight increase with respect to the ground state results (74 pN) conducted in the absence of oxidant, it is far from the conclusive distinction of two peaks at higher concentrations seen at 10^-4 M. We believe that molecules bound to the surface in the presence of oxidant exist in both ground and oxidized states. At lower concentrations of oxidant the former is dominant, resulting in the observation of a single peak. The increase in oxidant concentration by two orders of magnitude (i.e., from 10^-6 to 10^-4 M) results in the increased likelihood of oxidized molecules being probed, making the second peak more prominent. The trend of increasingly distinguishable results with oxidant concentration reaches a feasibility limit given that higher concentrations of Fe(ClO₄)₃ have been observed to degrade the molecule over the time necessary to conduct probing experiments.

Each AFM force spectroscopy probing experiment is conducted with freshly prepared solution, new SiO₂ wafers containing R⁴⁺, and new AFM probing tips to optimize the reproducibility of this study. Probing includes the specific binding of the tether of the [2]rotaxane R⁴⁺ molecule to the tip and involves the irreversible rupture of the molecule. Data are gathered until the binding yield decreases significantly, irrespective of probing location indicating a saturation of the AFM tip with ruptured molecules. Because rebinding is impossible, yield generally averages »30 points per experiment. Because of the high molecular costs of each experiment, which ensure a high level of control of experimental conditions, a thorough loading rate analysis, which includes several thousands of data points, is not feasible. In such a case, our hybrid analysis technique that combines feasible experimental data with well established numerical data to obtain a singular value becomes vital.

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